1 Data

The data is simulated as per the writeup here, except that \(\beta_k\), \(k = 1,2,3\) are fixed.

• Jointly simulated \(\epsilon_{ik}\) with \(\mu_k = \mathbf{0}\) and covariance \(\mathbf{\Sigma}\)
• It has 1000 households per year repeatedly collected for 30 years.

2 Analysis

We use Bayesian multivariate generalized linear models with correlated group-specific terms via Stan to model the binary outcomes

• Random intercept model: Assume an intercept that is different for each year

In other words, the fitted model was specified as:

\[y_{ijk} = \beta0_{jk} + \beta1_kx_i + \epsilon_{ik}\]

    model <- stan_mvmer(
        formula = list(
            y1bin ~ wealthindex + (1 | years) + (1 | hhid)
            , y2bin ~ wealthindex + (1 | years) + (1 | hhid)
            , y3bin ~ wealthindex + (1 | years) + (1 | hhid)
        )
        , data = sim_dflist[[1]]
        , family = list(binomial, binomial, binomial)
    )

3 Results